Made available in DSpace on 2015-04-22T22:16:08Z (GMT). No. of bitstreams: 1 Dissertacao Jose Mir Final.pdf: 1095442 bytes, checksum: bd21928f8f84d5235ab2e76eb5c5f0cb (MD5) Previous issue date: 2009-04-17 / FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas / The present work aims to evaluate some information criteria for the selection of models in the context of finite mixtures of skew-normal distributions. The analyzed criteria are the Akaike s Information Criterion - AIC, the Bayesian Information Criterion - BIC and the Efficient Detection Criterion - EDC. The evaluation concerning the performance presented by these criteria was obtained through a simulation study, on which the EM algorithm is required to find the maximum likelihood estimates of for the parameters of the model where the criteria are applied. It was also performed an experiment for the application of the theory developed, modeling a real data set previously analyzed in the specific literature. The results obtained point that, in an asymptotic sense, the three criteria tend to correctly evaluate the number of necessary components, but for small samples the AIC presents inferior performance than BIC or EDC. / Este trabalho tem por objetivo avaliar alguns critérios de informação para seleção de modelos no contexto de misturas finitas de normais assimétricas. Os critérios analisados foram o Critério de Informação de Akaike-AIC , Critério de Informação Bayesiano - BIC e Critério de Determinação Eficiente - EDC . A avaliação feita a respeito do desempenho apresentado por estes critérios se deu através de um estudo de simulação, em que utilizamos o algoritmo EM para encontrarmos as estimativas de máxima verossimilhança para os parâmetros do modelo com as quais empregamos os critérios. Foi também realizado uma aplicação da teoria desenvolvida para uma modelagem com dados reais utilizando dois conjuntos de dados já analisado anteriormente na literatura. Os resultados obtidos indicaram que, assintoticamente, os três critérios tendem a avaliar corretamente o número de componentes necessárias, mas para amostras pequenas o AIC apresenta desempenho inferior ao BIC e EDC, sendo que os dois últimos apresentam desempenho muito semelhante.

楚於資訊爆炸的時代，金融市場上彼此間更是息息相關的，有牽一髮而動全身的可能性。。因此在探討各種金融商品投資報酬率的分配時，只用單維分配函數來推估已經是得不到足夠的資訊，所以將考慮對資料配適關聯結構。 關聯結構有許多不同的種類變化，然而何種關聯結構才是最適合資料型態呢？為了瞭解二元的關聯結構是否配適的適當，將以AIC與卡方適合度檢定的方法進行關聯結構的檢驗。 首先以蒙地卡羅模擬法進行檢驗，藉由模擬觀察此兩種方法的結論是否能夠相信。最後以台灣股票市場中水泥類股、鋼鐵類股以及營造建材類股三類股兩兩間的當日交易資料的投資報酬率進行配適關聯結構，投資報酬率計算的頻率分為半點、整點以及兩點三種。配適出的結果為水泥類股、鋼鐵類股以及營造建材類股三類股間兩兩服從t關聯結構，自由度為三，除了頻率為半小時的水泥類與營造建材類以及鋼鐵類與營造建材類兩組。

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The minimum description length (MDL) principle originated from data compression literature and has been considered for deriving statistical model selection procedures. Most existing methods utilizing the MDL principle focus on models consisting of independent data, particularly in the context of linear regression. The data considered in this thesis are in the form of repeated measurements, and the exploration of MDL principle begins with classical linear mixed-effects models. We distinct two kinds of research focuses: one concerns the population parameters and the other concerns the cluster/subject parameters. When the research interest is on the population level, we propose a class of MDL procedures which incorporate the dependence structure within individual or cluster with data-adaptive penalties and enjoy the advantages of Bayesian information criteria. When the number of covariates is large, the penalty term is adjusted by data-adaptive structure to diminish the under selection issue in BIC and try to mimic the behaviour of AIC. Theoretical justifications are provided from both data compression and statistical perspectives. Extensions to categorical response modelled by generalized estimating equations and functional data modelled by functional principle components are illustrated. When the interest is on the cluster level, we use group LASSO to set up a class of candidate models. Then we derive a MDL criterion for this LASSO technique in a group manner to selection the final model via the tuning parameters. Extensive numerical experiments are conducted to demonstrate the usefulness of the proposed MDL procedures on both population level and cluster level.

The minimum description length (MDL) principle originated from data compression literature and has been considered for deriving statistical model selection procedures. Most existing methods utilizing the MDL principle focus on models consisting of independent data, particularly in the context of linear regression. The data considered in this thesis are in the form of repeated measurements, and the exploration of MDL principle begins with classical linear mixed-effects models. We distinct two kinds of research focuses: one concerns the population parameters and the other concerns the cluster/subject parameters. When the research interest is on the population level, we propose a class of MDL procedures which incorporate the dependence structure within individual or cluster with data-adaptive penalties and enjoy the advantages of Bayesian information criteria. When the number of covariates is large, the penalty term is adjusted by data-adaptive structure to diminish the under selection issue in BIC and try to mimic the behaviour of AIC. Theoretical justifications are provided from both data compression and statistical perspectives. Extensions to categorical response modelled by generalized estimating equations and functional data modelled by functional principle components are illustrated. When the interest is on the cluster level, we use group LASSO to set up a class of candidate models. Then we derive a MDL criterion for this LASSO technique in a group manner to selection the final model via the tuning parameters. Extensive numerical experiments are conducted to demonstrate the usefulness of the proposed MDL procedures on both population level and cluster level.

This thesis develops two variant statistical models for count data based upon compound models for contexts when the counts may be viewed as derived from two generations, which may or may not be independent. Unlike standard compound models, the variants model the sum of both generations. We consider cases where both generations are negative binomial or one is Poisson and the other is negative binomial. The first variant, denoted SVA, follows a zero restriction, where a zero in the first generation will automatically be followed by a zero in the second generation. The second variant, denoted SVB, is a convolution model that does not possess this zero restriction. The main properties of the SVA and SVB models are outlined and compared with standard compound models. The results show that the SVA distributions are similar to standard compound distributions for some fixed parameters. Comparisons of SVA, Poisson hurdle, negative binomial hurdle and their zero-inflated counterpart using simulated SVA data indicate that different models can give similar results, as the generating models are not always selected as the best fitting. This thesis focuses on the use of the variant models to model citation counts. We show that the SVA models are more suitable for modelling citation data than other previously used models such as the negative binomial model. Moreover, the application of SVA and SVB models may be used to describe the citation process. This thesis also explores model selection techniques based on log-likelihood methods, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The suitability of the models is also assessed using two diagrammatic methods, randomised quantile residual plots and Christmas tree plots. The Christmas tree plots clearly illustrate whether the observed data are within fluctuation bounds under the fitted model, but the randomised quantile residual plots utilise the cumulative distribution, and hence are insensitive to individual data values. Both plots show the presence of citation counts that are larger than expected under the fitted model in the data sets.

Made available in DSpace on 2014-06-12T18:01:37Z (GMT). No. of bitstreams: 2 arquivo6698_1.pdf: 1066555 bytes, checksum: db4d02aef759ceeda67e4d16ca74b282 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2011 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta tese aborda aspectos de modelagem e inferência em regressão beta, mais especificamente melhoramentos do teste de razão da verossimilhanças e proposição e investigação de critérios de seleção de modelos. O modelo de regressão beta foi proposto por Ferrari e Cribari-Neto [2004. Beta regression for modeling rates and proportions. J. Appl. Statist. 31, 799 815] para modelar variáveis contínuas no intervalo (0;1), como taxas e proporções. No primeiro capítulo, abordamos o problema de inferência em pequenas amostras. Focamos no melhoramento do teste da razão de verossimilhanças. Consideramos correções de segunda ordem para a estatística da razão de verossimilhanças em regressão beta em duas abordagens. Determinamos, por meio de uma abordagem matricial, o fator de correção de Bartlett e também uma correção de Bartlett Bootstrap. Comparamos os testes baseados nas estatísticas corrigidas com o teste da razão de verossimilhanças usual e com o teste que utiliza o ajuste de Skovgaard, que já está proposto na literatura. Os resultados numéricos evidenciam que as correções de Bartlett são mais acuradas do que a estatística não corrigida e do que o ajuste de Skovgaard. No segundo e terceiro capítulos, expandimos o modelo de regressão beta proposto por Ferrari e Cribari-Neto, considerando um modelo que assume que o parâmetro de dispersão, assim como o parâmetro de média, varia ao longo das observações e pode ser modelado por meio de uma estrutura de regressão. Com isso, surge o problema da seleção de variáveis, tanto para a estrutura da média quanto para a da dispersão. Esse assunto é tratado em dois capítulos independentes e auto-contidos, porém, ambos relacionados. No Capítulo 2 propomos critérios de seleção para modelos com dispersão variável e investigamos, por meio de simulação de Monte Carlo, os desempenhos destes e de outros critérios de seleção em amostras de tamanho finito. Percebemos que o processo de seleção conjunta de regressores para a média e para a dispersão não é uma boa prática e propomos um esquema de seleção em duas etapas. A seleção de modelos com o esquema proposto, além de requerer um menor custo computacional, apresentou melhor desempenho do que o método usual de seleção. Dentre os critérios investigados encontra-se o critério de informação de Akaike (AIC). O AIC é, sem dúvida, o critério mais conhecido e aplicado em diferentes classes de modelos. Baseados no AIC diversos critérios têm sido propostos, dentre eles o SIC, o HQ e o AICc. Com o objetivo de estimar o valor esperado da log-verossimilhança, que é uma medida de discrepância entre o modelo verdadeiro e o modelo candidato estimado, Akaike obtém o AIC como uma correção assintótica para a log-verossimilhança esperada. No entanto, em pequenas amostras, ou quando o número de parâmetros do modelo é grande relativamente ao tamanho amostral, o AIC se torna viesado e tende a selecionar modelos com alta dimensionalidade. Ao considerarmos uma estrutura de regressão também para o parâmetro de dispersão introduzimos um maior número de parâmetros a serem estimados no modelo. Isso pode diminuir o desempenho dos critérios de seleção quando o tamanho amostral é pequeno ou moderado. Para contornar esse problema propomos no Capítulo 3 novos critérios de seleção para serem usados em pequenas amostras, denominados bootstrap likelihood quasi-CV (BQCV) e sua modificação 632QCV. Comparamos os desempenhos dos critérios propostos, do AIC e de suas diversas variações que utilizam log-verossimilhança bootstrap por meio de um extensivo estudo de simulação. Os resultados numéricos evidenciam o bom desempenho dos critérios propostos

Habitat modeling can assist in managing potentially widespread but poorly known biological resources such as the federally endangered Delmarva fox squirrel (DFS; Sciurus niger cinereus). The ability to predict or identify suitable habitat is a necessary component of this species' recovery. Habitat identification is also an important consideration when evaluating impacts of land development on this species distribution, which is limited to the Delmarva Peninsula. The goal of this study was to build a predictive model of DFS occurrence that can be used towards the effective management of this species. I developed 5 a'priori global models to predict DFS occurrence based on literature review, past models, and professional experience. I used infrared photomonitors to document habitat use of Delmarva fox squirrels at 27 of 86 sites in the southern Maryland portion of the Delmarva Peninsula. All data were collected on the U.S. Fish and Wildlife Service Chesapeake Marshlands National Wildlife Refuge in Dorchester County, Maryland. Preliminary analyses of 27 DFS present (P) and 59 DFS absent (A) sites suggested that DFS use in my study area was significantly (Wilcoxon Mann-Whitney, P < 0.10) correlated with tree stems > 50 cm dbh/ha (Pmean = 16 + 3.8, Amean = 8+ 2.2), tree stems > 40 cm dbh/ha (Pmean = 49 + 8.1, Amean = 33 + 5.5), understory height (Pmean = 11 m + 0.8, Amean = 9 m + 0.5), overstory canopy height (Pmean = 31 m + 0.6, Amean = 28 m + 0.6), percent overstory cover (Pmean = 82 + 3.9, Amean = 73 + 3.1), shrub stems/ha (Pmean = 8068 + 3218, Amean = 11,119 + 2189), and distance from agricultural fields (Pmean = 964 m + 10, Amean = 1308 m + 103). Chi-square analysis indicated a correlation with shrub evenness (observed on 7% of DFS present sites and 21% of DFS absent sites). Using logistic regression and the Information Theoretic approach, I developed 7 model sets (5 a priori and 2 post hoc) to predict the probability of Delmarva fox squirrel habitat use as a function of micro- and macro-habitat characteristics. Of over 200 total model arrays tested, the model that fit the statistical, biological, and pragmatic criteria postulated was a post hoc integrated model: DFS use = percent overstory cover + shrub evenness + overstory canopy height. This model was determined to be the best of its subset (wi = 0.54), had a high percent concordance (>75%), a significant likelihood ratio (P = 0.0015), and the lowest AICc value (98.3) observed. Employing this predictive model of Delmarva fox squirrel occurrence can benefit recovery and consultation processes by facilitating systematic rangewide survey efforts and simplifying site screenings. / Master of Science

處於資訊變化迅速的時代，金融市場上彼此間更是息息相關的，因此在探討各種金融商品投資報酬率的分配時，只用單維分配函數來推估已經是得不到足夠的資訊，在此本研究使用關聯結構（copula）來推估投資報酬率的分配情形。 首先，透過蒙地卡羅(MC)模擬方法來探討Akaike Information Criterion （以下採"AIC"簡稱）法與卡方適合度檢定法檢驗關聯結構是否適合，進行檢驗隨機選取的資料是否服從其相對應的關聯結構。 本文共模擬五種關聯結構，分別為常態、t、Gumbel、Clayton、Frank關聯結構，其中AIC法在邊際分配為已知或未知下，在不同的參數設定值下，在所配適的關聯結構下所得到的AIC值最小，說明AIC法適合檢驗資料的關聯結構。另外卡方檢定法中，在已知邊際分配與未知邊際分配拒絕虛無假設的比例皆很接近設定的顯著水準，表示卡方適合度檢定法適合檢驗資料的關聯結構，而參數估計值的部分，當分割的格子越大，其所相對應的參數估計值會越不準確，且與設定的參數差距有擴大的現象。 最後以台灣股票市場中，內需產業較有影響的水泥類﹑鋼鐵類﹑營造建材類三種類股彼此間的投資報酬率進行配適關聯結構，投資報酬率時點的選擇以一天1/2天，1/3天，1/6天，1/9天，1/18天，1/27天，1/54天作為分割，分割成八種時點作為探討比較，其中AIC法所得到的結果皆以配適t關聯結構較為恰當，再以AIC法的結果，採用卡方t關聯結構，自由度採用3跟4輔助檢驗，然而卡方在5﹑10﹑15分鐘全部拒絕，在30分鐘後，除了鋼鐵與營建類的配對在30﹑45分鐘仍然拒絕，其他的部分都與AIC法符合。 關鍵字：關聯結構、蒙地卡羅(MC)模擬、AIC法、卡方適合度檢定、投資報酬率

The indispensability of the Church [in Africa] is the primary motive for the writing of this dissertation. Throughout the centuries, we have seen the Church in various contexts, and in many forms. We have borne witness to the good, bad and the ugly throughout the history of the Church. It is my belief that any constructive growth for the future success of the Church in Africa has to come from the bold recognition that if it is to succeed and fully partake in the Missio Dei, 'everything must change' (McLaren 2007). There is need for continuity and discontinuity; however, change is not negotiable!! The Church is called to be both confessional and Missional; the Church should always be forming (ecclesia simper formanda), and reforming (ecclesia simper reformanda)(van Gelder 2007). Therefore, there is a need to rediscover the essence of Jesus‟ intention for the Church; that is God‟s redeemed people, and their view of God‟s Kingdom with its various implications for an African Missiology. There is a need for Missional Churches in Africa, for dialogue, and for unity in action. In this dissertation, I will endeavour to present architecture for a Missional Ecclesiology in dialogue with Bosch; focusing on the emerging renaissance of African Missiology, and the current Pneumatological importance/ emphasis in many African Churches (otherwise known as African independent Churches- AIC). I have used the word architecture to mean overall framework emphasizing relationships between components, orientation and support as well as the innovative response to functional necessity. The focus/ niche of this dissertation will be faith communities in Botswana, because that is my current context of ministry, and there is an obvious research gap in this area of study as nothing has been researched and published in terms of an emerging Missional Ecclesiology amongst faith communities in Botswana. I will seek to collect, analyze and interpret current as well as historical data regarding Church (mission), population and emerging areas of concern for faith communities in Botswana, and, by implication, Southern Africa. / Dissertation (MA(Theol))--University of Pretoria, 2010. / Science of Religion and Missiology / unrestricted